As the other answers have stated, genuine faith results in works, but works are not necessary for salvation. This was true of Abraham who, having believed God, offered his son Isaac. It was not his work that saved him, but his saving faith, which prompted works.

James also speaks of this:

But someone may well say, “You have faith and I have works; show me your faith without the works, and I will show you my faith by my works.” James 2:18 NASB

As James asserts later, a faith that produces no works is no faith at all:

For just as the body without the spirit is dead, so also faith without works is dead. James 2:26 NASB

So, the faith of Zacchaeus resulted in works. He seeks Jesus out, calls Him "Lord", then exhibits the fruit of repentance in his acts of righting the wrongs he had committed.